It wouldn't be called "the satellite paradox" if it did what you would naively expect. :-)

If you have 2 objects in the same orbit and one accelerates backwards, that one winds up below and in front of the first. This happens because accelerating backwards causes it to lose energy, so it falls, and in falling picks up more kinetic energy than it had before.

It depends on the frame of reference. Obviously we're talking about a solar reference frame here with respect to linear velocity (it's the only other object), but it will also be rotating.

If the reference frame is initially rotating at with your orbit or a closer one, "speed up" is accurate. If it's rotating with some more distant orbit, "slow down" is accurate.

This, by the way, is one reason why physicists tend to just say "accelerate" in both cases: then, it's technically true for any external reference frame.

You will slow down until you are stationary with respect to distance from the sun, and then start accelerating towards it, ie, falling.